Digital twins of bridges rely on physics-based models to infer full-field structural responses from sparse monitoring data. The reliability of these predictions depends on the calibration of model parameters while accounting for discrepancies between the model and the physical system. Such discrepancies, commonly referred to as model-form uncertainty (MFU), arise from simplifying assumptions and incomplete representations of physical processes, and can substantially affect predictive reliability. Explicitly quantifying MFU during calibration is therefore essential for trustworthy digital-twin predictions. This work presents a calibration framework that explicitly represents MFU through stochastic parameter embedding. The framework is demonstrated using a simplified two-dimensional cross-sectional thermal model of the Nibelungenbrücke calibrated against temperature measurements from its monitoring system. By explicitly accounting for MFU, the proposed methodology enables computationally efficient models to be reliably employed within digital-twin environments while maintaining predictive credibility. The framework introduces a three-step calibration strategy that progressively addresses sources of discrepancy while maintaining a clear distinction between identified uncertainties. Variance decomposition is used to characterize the structure of predictive uncertainty and its propagation to quantities of interest. Remaining discrepancies between predictive distributions and observations are quantified using Kolmogorov-Smirnov metrics to assess predictive consistency across seasonal conditions. The results demonstrate that explicitly accounting for MFU improves the interpretability and reliability of predictive uncertainties and validate the methodology for calibration of physics-based models supporting digital twins in structural health monitoring.

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